Preheat your oven to 400°F. Arrange the zucchini, eggplant, and cherry tomatoes on a baking sheet. Drizzle with the 2 tablespoons olive oil and season with kosher salt and freshly ground black pepper. Roast the vegetables for 30 minutes, or until all are tender and the eggplant is browning. Reduce the oven temperature to 350°F.
While the vegetables roast, bring a pot of salted water to a boil. Cook the pasta al dente, according to package instructions.
Lightly oil a 9 by 13- inch/24 by 36cm rectangle pan. Spread a half cup (120ml) of the marinara sauce lightly across the bottom.
Drain the cooked pasta. Spread one third of the pasta in the baking dish, followed by a third of the vegetables. Dollop 2/3 cup of the vegan ricotta over the pasta and vegetables, followed by 1 1/3 cups marinara sauce. Repeat this twice. Use the back of a spatula or spoon to lightly spread and swirl around the marinara and vegan ricotta along the top when you finish layering. Then, sprinkle this layer with the vegan parmesan cheese.
Cover the pasta with foil and bake it for 20 minutes. Uncover and bake for another 15-25 minutes, or until bubbling at the edges and crisping on the top. Cut into slices and serve or store.